Compound bursting dynamics in a parametrically and externally excited mechanical system

This paper aims to report complex bursting dynamics in a parametrically and externally excited mechanical system. Typically, two compound bursting patterns, i.e., bursting of "supHopf/homoclinic-fold/supHopf" type and bursting of "supHopf/supHopf-fold/supHopf" type, composed of two different clusters during each period of bursting, can be observed in this system. To begin with, the generation of each of the two clusters in compound bursting of "supHopf/homoclinic-fold/supHopf" type is investigated by the fast-slow analysis. Then, a two-parameter bifurcation diagram is plotted to investigate the transition of the compound bursting. We show that there are two originally disunited active areas, which may inosculate as a whole by homoclinic bifurcations if the system parameter varies properly. Based on this, a different type of compound bursting, i.e., bursting of "supHopf/supHopf-fold/supHopf" type, is revealed. (C) 2020 Elsevier Ltd. All rights reserved.